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标题：Positive ground states for nonlinearly coupled Choquard type equations with lower critical exponents
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作者：Huiling Wu
期刊名称：Boundary Value Problems
印刷版ISSN：1687-2762
电子版ISSN：1687-2770
出版年度：2021
卷号：2021
期号：1
页码：1
DOI：10.1186/s13661-021-01491-z
出版社：Hindawi Publishing Corporation
摘要：We study the coupled Choquard type system with lower critical exponents $$ \textstyle\begin{cases} -\Delta u \lambda _{1}(x)u=\mu _{1}(I_{\alpha }* \vert u \vert ^{ \frac{N \alpha }{N}}) \vert u \vert ^{\frac{\alpha }{N}-1}u \beta (I_{\alpha }* \vert v \vert ^{ \frac{N \alpha }{N}}) \vert u \vert ^{\frac{\alpha }{N}-1}u,\quad x\in {\mathbb{R}}^{N}, \\ -\Delta v \lambda _{2}(x)v=\mu _{2}(I_{\alpha }* \vert v \vert ^{ \frac{N \alpha }{N}}) \vert v \vert ^{\frac{\alpha }{N}-1}v \beta (I_{\alpha }* \vert u \vert ^{ \frac{N \alpha }{N}}) \vert v \vert ^{\frac{\alpha }{N}-1}v,\quad x\in {\mathbb{R}}^{N}, \\ u, v\in H^{1}({\mathbb{R}}^{N}), \end{cases} $$ where $N\ge 3$ , $\mu _{1}, \mu _{2}, \beta >0$ , and $\lambda _{1}(x)$ , $\lambda _{2}(x)$ are nonnegative functions. The existence of at least one positive ground state of this system is proved under certain assumptions on $\lambda _{1}$ , $\lambda _{2}$ .
关键词：Choquard system ; Lower critical exponent ; Positive ground state